Analytic Graphics

Princliples of Analytic Graphics

We are trying to tell a story about what is happening in the data. This is achieved via the following principles

Showing comparisons

Evidence for a hypothesis is always relative to a competing hypothesis (\(H_A\) vs \(H_0\)). Any evidence that you provide or any data summary must be able to also answer the question, “Compared to what?”

(The example in the lecture is unavailable for reproduction; this is my own)

We may believe that more car cylinders lead to a higher mpg. mtcars contain this information

data(mtcars)

Our competing hypotheses may be
\(H_0\): There is no difference in the mpg between cars with 4 and 6 cylinders
\(H_A\): There is a difference in the mpg between cars with 4 and 6 cylinders

boxplot(mpg~cyl, data = mtcars[(mtcars$cyl==4)|(mtcars$cyl==6),], xlab="#cylinders", ylab="miles per galon" )

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Showing causality, mechanism, and systematic structure

“Causality” isn’t meant to be taken literally here; it’s more of a statement of how you believe the world works. For example, if installing an air cleaner in the homes of asthmatic children increased the number of their symptom-free days, we could hypothesize that less particulate matter is entering the child’s lungs and triggering symptoms. In this case, we could show a plot that may corroborate that point of view, such plotting side by side the number of symptom free days and the amount of household particulate matter. To really confirm the hypothesis, we would have to do an experiment.

In the mtcars example, we could theorize that the unexpected result is due to the fact that cars with a higher number of cylinders also weigh more, and so, the mpg decrease

par(mfrow = c(1, 2))
boxplot(mpg~cyl, data = mtcars[(mtcars$cyl==4)|(mtcars$cyl==6),], xlab="#cylinders", ylab="Miles per galon" )
boxplot(wt~cyl, data = mtcars[(mtcars$cyl==4)|(mtcars$cyl==6),], xlab="#cylinders", ylab="Weight (lb/1000)" )

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The spread of the weight for cars with 4 cylinders is significantly lower than that of cars with 6 cylinders. This does seem to corroborate the view that the lower mpg is due to an increase in the weight

Show multivariate data

Basically, show as much data on a single plot as is possibly reasonable. This allows us to tell a much richer story.

Integrate as many modes of evidence as you can.

This means competely integrating words, numbers, images and plots

Describe and document the evidence with appropriate labels, scales, sources…you need to add credibility to your story!

Plotting Systems

The process of making a plot involves several considerations, such as

Where will the plot be made? On the screen? Or in a file?
How will it be used? For temporary viewing on a screen? In a web browser? Or in a paper, or for a presentation?
Is there a large amount of data that will go into this plot?
Will it be necessary to dynamically resize it?

Base

This is the most commonly used system in R. Plots using the Base system involve two steps

Initializing the plot
Annotating the plot

The many parameters of the Base system are documented in ?par.

Initialization examples: We need to know how to make

Histograms: hist()

hist(x = airquality$Ozone)

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Scatterplots: with(data=, plot(colname1, colname2))

with(data = airquality, plot(Wind, Ozone) )

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Box-and-whisker plots:

step 1: set factors as necessary
step 2: boxplot(variable~factor (ie: y vs x), data)

# Change month into a factor variable, and overwrite the month column
airquality<-transform(airquality, Month<-as.factor(Month)) 
boxplot(Ozone~Month, data = airquality)

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Annotation examples text() adds labels within the plot axis() specify axis ticks

title() adds titles.

with(airquality, plot(Wind, Ozone))
title(main = "Ozone and wind in NYC", xlab = "Wind", ylab = "Ozone")

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The second line isn’t really necessary, however

with(airquality, plot(Wind, Ozone, main="Wind vs. Ozone in NYC"))

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points() adds points

Suppose we wanted to highlight the points that all come from the month of May 1. construct the plot 2. use with (data=subsetted data frame, points(col1, col2, color = ))

with(airquality, plot(Wind, Ozone, main="Wind vs. Ozone in NYC"))
with(data = subset(airquality, Month==5), points(Wind, Ozone, col = "blue"))

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legend() adds a legend

#type="n" initiallizes the graphics device, but does not output anything
with(airquality, plot(Wind, Ozone, main="Wind vs. Ozone in NYC", type="n"))

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with(airquality, plot(Wind, Ozone, main="Wind vs. Ozone in NYC", type="n"))
with(data = subset(airquality, Month==5), points(Wind, Ozone, col = "blue"))
with(data = subset(airquality, Month!=5), points(Wind, Ozone, col = "red"))
legend(x = "topright", pch=1, col=c("blue", "red"), legend = c("May", "Other Months"))

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Add a line with abline()

with(airquality, plot(Wind, Ozone, 
                      main="Wind vs. Ozone in NYC", type="n"))
with(data = subset(airquality, Month==5), points(Wind, Ozone, 
                                                 col = "blue"))
with(data = subset(airquality, Month!=5), points(Wind, Ozone, 
                                                 col = "red"))
legend(x = "topright", pch=1, col=c("blue", "red"), 
       legend = c("May", "Other Months"))
abline(lm(Ozone~Wind, airquality))

plot of chunk unnamed-chunk-12 Multiple Base plots are drawn by first splitting the graphics device with par(), and then calling plot() as many times as necessary. In this case, we may need a label to cover the entire panel of plots with mtext(text, outer= T). For this to work, the outer margins must be adjusted

par(mfrow = c(1,2), mar = c(4,4,2,1), oma=c(0,0,2,0))
with(data = airquality, {
        plot(Wind, Ozone, main="Wind vs Ozone")
        plot(Wind, Solar.R, main="Wind vs Solar Radiation")
})
mtext(text = "Wind vs Different things", outer = T)

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Lattice plotting system

The Lattice plotting system is particularly useful for plotting high dimensional data, and for making many, many plots at once.

Unlike the Base system, which plots directly to the graphics device, Lattice functions return an object of class trellis. This object is printed to the graphics device. The object can be saved to an R obeject, but there’s no real need to ever do this.

Main functions

xyplot(y-axis~x-axis, | conditioning cariables, data = some data frame) <-scatterplots

library(lattice)
xyplot(x = Ozone~Wind, data = airquality)

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airquality<-transform(airquality, Month<-factor(Month))
xyplot(x = Ozone~Wind|Month, data = airquality, layout = c(5,1))

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set.seed(10)
x=rnorm(100)
f<-rep(0:1, each=50); f

##   [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
##  [36] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
##  [71] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

y=x+f-f*x+rnorm(100, sd = .5)
f<-factor(x = f, labels = c("group 1", "group 2"))
xyplot(x = y~x|f, layout = c(2,1))

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xyplot(x = y~x|f, panel = function(x, y, ...){
        panel.xyplot(x, y, ...)#first call the default panel function to make the points appear
        panel.abline(h = median(y)) # add a horizontal line
})

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2. bwplot() <-box and whiskers plots

attach(mtcars)
gear.f<-factor(gear,levels=c(3,4,5),
          labels=c("3gears","4gears","5gears")) 
cyl.f <-factor(cyl,levels=c(4,6,8),
   labels=c("4cyl","6cyl","8cyl")) 
bwplot(cyl.f~mpg|gear.f, layout=(c(1,3)))

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dotplot(cyl.f~mpg|gear.f, 
          main="Dotplot Plot by Number of Gears and Cylinders",
   xlab="Miles Per Gallon")

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ggplot2

This package implemets Wilkinson’s Grammar of Graphics. It was written by Wickham. The grammar of graphics represents abstaractions of graphics ideas and objects. The grammar tells us that a statistical graphic is a mapping from data to an aesthetic attribute (colour, shape, size), geometric objects (like points, lines and bars). Factors are very important for indicating subsets of your data. These should be labeled. qplot() (the quick plot) is the workhorse function. ggplot() is the core function, and very flexible for doing things that qplot cannot do.

How to use qplot()

library(ggplot2)

## 
## Attaching package: 'ggplot2'
## 
## The following object is masked from 'mtcars':
## 
##     mpg

# scatterplot
qplot(x = wt, y = mpg, data = mtcars)